The present invention relates to time domain reflectometry, and more particularly to a method of estimating fiber loss per unit distance and return signal power at a given point efficiently from a sampled return signal acquired by an optical time domain reflectometer (OTDR).
In an OTDR a laser pulse is injected into an optical fiber and a photosensitive detector receives the light that returns due to Rayleigh backscattering. Ideally the optical power of the received signal is EQU P=A.times.10.sup.-Lnd/5 (1)
where A is the power of the return signal at an injection point (n=0), L is the one-way loss in units of decibels per kilometer (fiber loss), d is the sampling period in kilometers, and n is the sample index. In a real system this ideal signal is corrupted by additive Gaussian white noise that adds a component, v(n), to the optical power of the received signal. Since the return signal is exponentially decaying, it is quickly buried in the receiver background noise, making the determination of fiber characteristics in the noisy region very difficult.
Two of the primary measurements in optical reflectometry are the values of A and L. The standard technique for measuring these unknowns is to fit a line, defined by the expression Mn+B, in the least squares sense to the logarithm, base ten, of the signal defined in equation (1). Were the signal noiseless, this results in M=-Ld, from which L is immediately available, and in B=51 ogA. But as the signal to noise ratio (SNR) decreases, M and B rapidly depart from the desired values and become biased and jittery from the noise. When the SNR drops below 5 dB, the bias becomes large and the variance, or jitter, becomes much greater than that demanded by the theoretical minimum. Moreover any negative data values coming from the noisy version of equation (1) must be thrown out since the logarithm is undefined.
What is desired is a method of estimating the values of fiber loss and return signal power in the presence of noise.